Changhui Tan
I am a postdoctoral research associate in CSCAMM and Department of Mathematics, University of Maryland.
A discontinuous Galerkin method on kinetic flocking models
Changhui Tan
Mathematical Models and Methods in Applied Sciences, Volume 27, No 7, pp. 1199-1221 (2017).
Abstract
We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker–Smale [Emergent behaviors in flocks, IEEE Trans. Autom. Control. 52 (2007) 852–862] and Motsch–Tadmor [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 144 (2011) 923– 947] models. We first establish a well-posedness theory and large-time flocking behavior for the kinetic systems, which indicates a concentration in velocity variable in infinite time. We then apply a discontinuous Galerkin method to treat the asymptotic \(\delta\)-singularity, and construct high-order positive-preserving schemes to solve kinetic flocking systems.
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doi:10.1142/S0218202517400139 |
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Download the Published Version |
List of publications
Preprint
- [6] Vinh Nguyen, Roman Shvydkoy, Changhui Tan.
Mean-field limits of deterministic and stochastic flocking models with nonlinear velocity alignment.
Submitted. - [5] Changhui Tan, Zhuan Ye.
Global well-posedness of the 2D primitive equations with fractional horizontal dissipation.
Submitted. - [4] Changhui Tan, Liutang Xue, Zhilong Xue.
A revisit of patch solutions for the 2D Loglog-Euler type equation.
Submitted. - [3] Elie Abdo, Quyuan Lin, Changhui Tan.
Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation.
Submitted. - [2] Kunhui Luan, Changhui Tan, Qiyu Wu.
On the Euler-Poisson equations with variable background states and nonlocal velocity alignment.
Accepted, to appear at SIAM Journal on Mathematical Analysis. - [1] Qiaoyun Miao, Changhui Tan, Liutang Xue, Zhilong Xue.
Local regularity and finite-time singularity for a class of generalized SQG patches on the half-plane.
Submitted.
Curriculum Vitae
Education
| 2008 – 2014 | Applied Mathematics and Scientific Computing (AMSC) Program |
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University of Maryland, College Park |
| Doctor of Philosophy, Major: Applied Mathematics | |
| 2004 – 2008 | Department of Scientific and Engineering Computing |
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School of Mathematical Sciences, Peking University |
| Bachelor of Science, Major: Applied Mathematics | |
| 2005 – 2008 | National School of Development |
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Peking University |
| A Double Major in Economics, Bachelor of Science |